Measures of full dimension on affine-invariant sets-Reference-Cited by-同舟云学术

Measures of full dimension on affine-invariant sets

Published:1996-04 Issue:2 Volume:16 Page:307-323
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

Kenyon R.,Peres Y.

Abstract

AbstractWe determine the Hausdorff and Minkowski dimensions of some self-affine Sierpinski sponges, extending results of McMullen and Bedford. This result is used to show that every compact set invariant under an expanding toral endomorphism which is a direct sum of conformal endomorphisms supports an invariant measure of full dimension.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference25 articles.

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2. On Weierstrass-like functions and random recurrent sets

3. Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation

4. Generating special Markov partitions for hyperbolic toral automorphisms using fractals

5. Self-replicating tilings

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